Rapid recovery pulse transformer circuit



Feb. 8, 1966 S. N, EINHORN ETAL RAPID RECOVERY PULSE TRANSFORMER CIRCUIT Filed Jan. 31, 1963 l R L Fig] PRIOR ART ii l n0 d x L Fig.2

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9 I2 I I 9 I DUE X T0 I INVENTORS. h ImDUE I X SIDNEY N. EINHORN T01 TB RICHARD C. WEISE 8USEC. ZUSES. o I 2 ATTORNEY United States Patent 3,234,407 I RAPID RECOVERY PULSE TRANSFORMER CIRCUIT Sidney N. Einhorn, Willow Grove, Pa., and Richard C.

Weise, Haddonfield, N.J., assignors to Burroughs Corporation, Detroit, Mich, a corporation of Michigan Filed Jan. 31, 1963, Ser. No. 255,386

12 Claims. (Cl. 307-.101)

The present invention relates to trans-former circuits employed in coupling pulses to a utilization system and, more particularly, to a pulse transformer circuit which coerces the rapid recovery of the transformer after the transmission-of an information pulse so that subsequent information pulses can be supplied properly to the utilization. system with only brief intervals therebetween.

The rapid transmission of information pulses through a transformer circuit is of significant importance in many modern electronic systems. The ability of such a system to speedily utilize the information it has received often exceeds, the rate at which an input transformer circuit coupled thereto can accept and properly relay the information. Therefore, the utilization system is forced to operate well below. its capacity. This results in such a significant loss of .time ,thatadditional apparatus may have, to be purchased to accomplish a task which otherwise could be handled easily by the basic system were it not hobbled by a sluggish pulse transformer circuit.

Ideally, the. time interval between applied information pulses should be only of that duration which is sufi'icient for the utilization system to recognize the discreteness of each pulse. However, when transformer coupling is employed to an input stage of such system, the intervals between inforrnation pulses must also be of sufiicient duration to allow for the complete decayof the magnetic field created in the transformer as a consequence of the receipt of a first pulse before it can be permitted to receive and transmit a. second pulse. 'If the magnetic field were not fully eliminated between these pulses, improper action could occur, t

The duration of suchdecay in most transformer circuits is at least as long as, and usually significantly longer than, an applied information pulse. .It is this time consuming decay period which the present invention is designed to overcome.

In brief, our invention comprises apparatus for applying input current pulses-information pulses and transformer neutralization pulses-alternately in opposite directions through a transformer primary coil, the neutralizationpulses of shorter duration than the information pulses, and pulse polarity responsive circuitry associatedwith the transformer secondary offering a path for the information pulses to an operative load and a path for the neutralization pulses to a dummy load. These elements cooperate such that the magnetic field remaining in the transformer due to the information pulse is fully eliminated atthe end of the neutralization pulse and at that time there is a zero resultant flux in the transformer. Thus the transformer is again in condition to accept and properly transmit a further information pulse.

It is,.therefore, an object of the present invention to provide'an improved pulse transformer circuit having a recovery time significantly shorter than that normally obtainable by such inductive circuits.

Another object-of this invention is to regulate and increase the duty factor of a transformer coupled between a ,source of stabilized constantcurrent pulses and an operative load.

Transformer circuits and other inductively coupled cir cuits employed for pulse transmission are often designed on the basis of the duty factor to which the coupling is expected to operate. Duty factor, as herein used, is de- ICC fined as the quotient of the pulse duration divided by the interval between like points of successive pulses and is,

duty factor increases toward unity which is obviously advantageous as the circuit is then more efiicient with respect to time consumption.

Recovery time is defined as the time necessary for the magnetic field created in the transformer, as a consequence of a pulse input, to completely collapse. Consequently, as the recovery time decreases, the interval between pulses can be decreased and accordingly the pulse delivery rate may increase. Hence a further object of this invention is to lessen recovery time and to cause the duty factor to increase toward unity.

The above mentioned objects and other objects and features of our invention will become more apparent by reference to the following description taken in conjunction with the accompanying drawings wherein:

FIG. 1 is a schematic diagram of a typical pulse transformer circuit known in the prior art;

FIG. 2 is a schematic diagram of an embodiment of the pulse transformer circuit of the present invention; and

FIG. 3 is a set of graphs of time versus amplitude for the currents applied to the primary, the magnetizing currents, and the voltages across the secondary of the circuits of FIGS. 1 and 2. The curves of a through c relate to FIG. 1 and d through h to FIG. 2.

FIG. 1 shows a conventional type of pulse transformer circuit well known in the prior art comprising a primary coil P connected to a source of information current pulses I a secondary coil S across which are connected in paral lel a damping resistor R and a series combination of a load resistor R and a diode D the diode being poled for conduction toward the load. The source I provides,

Let it also be assumed that the interwinding and distributed capacitance, as well as the leakage inductance, can be neglected.

When a current pulse, as shown in FIG. 3a, is applied to this circuit by the source l there will appear at the output a voltage pulse as shown in FIG. 3b. The latter pulse consists of a positive portion equal in duration to the applied current pulse, 8 microseconds, and a negative portion, the duration of which depends upon the particular parameters of the circuit. As shown, the negative portion of the voltage pulse decays slowly towards zero. This decay follows the same form and has the same duration as the collapsing magnetic field in the transformer. As previously stated, this duration is called the recovery time. Further, the magnetizing current rising to a peak of I is illustrated in FIG. 30.

It is well known that a transformer possessing a magnetic field is a repository of energy. Such energy due to an input I is proportional to the strength of the magnetic field and is represented by the equation As the magnetic field is collapsing, the magnetizing current I in the transformer is also decreasing with a resultant decay of the energy U. When the field is fully collapsed, the magnetizing current is at zero, and, as shown by the above equation, so. is the energy. It is, therefore, proper to state that the time it takes for the magnetic field to completely collapse is the same time necessary for the transformer energy to reach zero. Since the former was defined as the recovery time, it can also be said that the recovery time is that time during which the energy stored in the transformer changes from one level to a zero reference level.

As a practical expedient, a recovery of 99% is considered a practical complete recovery. Such recovery can be accomplished within five time constants and in the circuit of FIG. 1 would be computed as:

T =5 L /R =5 x 5 1O /300=83.33 microseconds It may be seen in the-example thus given that the maximum duty factor would be less than 0.1. As used, the term time constant has its normal meaning, i.e., that time during which an impressed quantity will decay to a value of l/e of its initial value.

-We are, of course, aware of the fact that some pulse transformer circuits have been developed which have faster recovery times than the circuit above discussed. However, those circuits frequently comprise numerous active and passive elements and are useful only in certain restricted types of pulse systems.

Our inventive pulse transformer circuit, an embodiment of which is illustrated in FIG. 2, has attributes which overcome the major disadvantages of the prior art. The transformer recovery of our inventive circuit is extremely fast and, in fact, may occupy an appreciably shorter time than the information pulse itself. Thus a system coupled to our transformer circuit can be very efiicient in its utilization of time. This novel circuit also has the advantages of simplicity, durability and adjustability.

As shown in FIG. 2, our circuit may comprise a center tapped primary coil having an upper coil segment P and a lower coil segment P To each coil segment is coupled a pulse source which preferably provides stabilized constant current pulses to its coil segment in the direction indicated by its associated arrow. To the segment P is coupled the pulse source I and to the segment P is coupled the pulse source I The sources supply pulses during mutually exclusive intervals. Provided further is a secondary coil S having a unity turns ratiowith each segment of the primary coil, by way of example and not to be construed as a limitation.

Across the secondary coil are three sets of parallel components. The first is a series combination of a variable dummy load resistor R and adiode D the diode poled for conduction toward the top or dotted end of the secondary coil. The second is a damping resistor R The "third is a series combination of an operative load resistor R and a diode D which is poled for conduction awayfrom the dotted end of the secondary coil.

Although the pulse sources I and '1 are shown in FIG. 2 as separate devices and, in fact, were so constructed in an operative arrangement of our invention, it would be permissible to employ instead a single pulse source capable of supplying discrete input pulses to the coil segments P and P respectively, during successive intervals, assuming that the source were capable of very rapid switching at time 1 and t as shown in FIG. 3. Another type of arrangement which could be used would be one, also with rapid switching means, that would be gated to drive an untapped primary coil with alternating pulses of opposite polarity.

We have found, however, that two simple current pulse sources, each connected exclusively to a different segment of a tapped primary coil, are more advantageous than a more complex pulse source connected across the untapped primary coil. Although two pulse sources might occupy more space and initially cost more than one source having a switching and/or phase changing network, the advantage of simplicity of two devices outweighs the possible disadvantages. These current pulse sources may comprise discharge or solid-state elements and may be constructed similar to many of the current pulse sources well known in the art.

In the operation of this circuit, let it be assumed that a positive stabilized constant current pulse of information, such as depicted by FIG. 3d; is supplied by the pulse source 1 to the coil segment P in the direction shown by its associated arrow in FIG. 2. The magnetizing current due solely to I is illustrated in FIG. 3g and would decay to the level marked x by time 1 even should 1 not be applied. The I pulse causes a magnetic field to build up in the trans-former because of the magnetizing current therethrough and thereby induces a positive voltage pulse across the secondary circuit be tween times t and t as shown in FIG. 3 This induced voltage causes a current to flow away from the dotted end of the secondary coil, through the diode D and to the operative load R as well as the damping resistor R At the termination of the information pulse, there remains in the transformer, because of its normal action, an appreciable quantity of flux. As earlier stated, this flux and the energy associated therewith should be eliminated before the next information pulse is applied, and the time necessary for this elimination is called the recovery time. p

In order to coerce the rapid collapse of the retained magnetic field, so that the next pulse of information can be applied by the source 1 as closely as possible to the prior information pulse from that source, the pulse source 1;, supplies a neutralization pulse as shown in FIG. 3e. This neutralization current pulse is preferably applied simultaneously with the termination of the information pulse and is in the reverse direction from the information pulse, since it is applied in the direction of the arrow associated with the source .1 as seen in FIG. 2..

The neutralization pulse causes a magnetic field, and the energy associated therewith, to tend to build up in the reverse direction in the transformer becauserof the magnetizing current I and tends to induce an associated voltage pulse of polarity opposite from that efiected by the information pulse. The resultant voltage pulse, as shown between the time and t of FIG. 31, urges a current flow out from the bottom of the secondary coil and through the series combination of the dummy load R and the diode D as well as the dampingresistor R both of which are across the secondary coil.

Because of thehigh inverse resistance of the diode D which is poled toward the dotted end of the secondary coiland the relatively large resistance of the damping resistor R as compared with the low resistance of the,

operative load R1,, an ineifectual amount of current will be directed to the dummy load during the pulsation from the source I Thus, during that time, the dummy load R is effectively isolated from the rest of the circuit. Also, because of the high inverse resistance of the diode D which is poled for conduction toward the bottom of thev secondary coil, and the disparity of resistance between the dummy load R and the damping resistor R the operative load R will receive virtually no current during the pulsation from the source 1 Thus the operative load R is effectively isolated from the rest of the circuit during that period of time. i

The magnetizing currents I elicited by the sources I, and l during the period between t, and t; are of opposite direction and have magnitudes at the termination of the respective pulses from the sources I and I which are dependent upon the durations of those pulses and the 7 equivalent resistance of the circuit at that time. From the above discussion, it will be apparent that during a pulse from the source 1,, the equivalent resistance 'in the secondary circuit will be R R /R -I-R and during the pulse from the source l itwill be R R /R -t-R Since the stored transformer energy U= /z'L I and since l depends upon pulse duration and resistance, the energy in the transformer at the endsofthe pulses from the sources I and I can be predetermined, as will be demonstrated hereinafter. a

From the foregoing it should now also be apparent to those skilled in the art that. the amount of energy stored in the transformer .by reason of the application of the information pulse will bealtered by the opposing energy developed as a consequence of the neutralization pulse. Hence, at the termination of the neutralization pulse, time t theenergy should be reduced substantially to zero.

This goal is attained by employing our invention circuit with the proper choice of parameters. With our invention, a specific recovery time can be arbitrarily chosen and then the necessary parameters includingthe level of current 1 determined wtih relative case. Also assuming a fixed set of parameters, the recovery time can be altered and regulated by changing only the value of the dummy load R ,which is shown in FIG. 2 as a variable resistor for this purpose. We have assumed, for simplicity, that the amplitudes of the pulses from the sources I and 1 are equal and, also, that turns ration between the coils P and S and the coilsP and Sboth are unity. Thus the turns ofP equal those of P These assumptions result in a unique numeric proportionality between the ratios of the durations of the information and neutralization pulses and the equivalent resistances during those pulses. Neither these assumptionsnor the numeric proportionality are to be considered restrictive. All that is desired in the proper operation of our invention is that the two magnetizing currents; which are caused bythe sourcesl and I cancel one another at the end of the pulse I i As will be apparent from the statements above and th examples below, the magnetizing currents depend upon the input pulse durations, the equivalent resistances, magnetizing' inductance and the magnitudes of the total secondary currents. The latter clearly depend upon the pulses from the current sources and the turns ration. Hence, these parameters can individually have any de sired values as long as they result in a proper value for their associated magnetizing current. It is again emphasized that thetime necessary for the energy in the transformerto attain a zero reference level is the recovery time. Therefore, if at time t the magnetizing current dueto the neutralizing current pulse is equal and opposite to the magnetizing current due to the information pulse,:therecoverytime is only the duration of the neutralization pulse (t t It will also now beapparent that the damping resistor I R which is actively coupled to the secondary coil during the pulsations from-both sources I and I critically damps the ringing of theentire output voltage pulse.

In exploring a mathematical explanation of the operation 'of this invention, the following formulas maybe considered: i i m o wherejU is the energy stored in the transformer during I and I is the magnetizing current at the end of I calculated in accordance with Formula 2,

I R R t rants *1) d where the magnetizing. current in the absenceof I decays from a peak I to I duringthe period between t and t nk-I'D from which the relationship of R may be calculated.

It may also be shown that a convenient method of choosingR exists simply by adjusting its value until the areas under the voltage waveform of FIG. 3f are equal. This exist-s when the field is completely cancelled and it will be observed that the trailing edge of I returns to zero with no overshoot or undershoot.

Equation number one relates the energy to the magnetizing current from which'it may be seen that a reduction of the current to zero likewise reduces the energy to zero.

Equation number two sets forth the solution for the magnetizing current I at the end of the information pulse t during which time the'operative load R forms part of the equivalent resistance. This equation contains the same parameters for both the/prior art circuit and the circuit ofFIG. 2. r v s Equation number three sets forth the solution for the magnetizing current I at the end of the deene'rgization pulse t during which time the dummy load R forms part of the equivalent resistance.

Since forthe optimum operation ofiour circuit the two magnetizing current-s I and L, (due to I havetlie same magnitude, the value of R may be calculated from equation'four. s

The magnitude of magnetizing current I is determined by the solution of equation number two. An arbitrarily chosen recovery time (t -t may be substituted into equation number three with the determined value of I to ascertain the necessary value of the dummy load R To obtain a duty factor of eight-tenthsin the given example, the duration :of the neutralization pulse, which we assume to be the same as the intervalfbetween pulses, should be two microseconds. Given the stated parameters and (t t .equal. to two microseconds, the solution of equation four provides a resistive value for the dummy load. i .i l l Ifa recovery time, i.e., a neutralization pulseduration, of one microsecond were desired so as to produce a duty factor. of almost nine-tenths, all that needs to be done to'the circuitparameters is. to alter .theuvalue-of the dummy load R as determined by u lattermost formula by substituting therein thenewvalue of one microsecond for the neutralization; pulse duratio nf(t t Since the parameters of equation number two are not changed, the magnetizing current I remains the same. i

It has been observed experimentally and can be verified mathematically that the voltage waveform of the secondary will attain azero DC, level at the termination of each neutralization pulse if. the proper circuit parameters are employed. -Henee,; as has been said, another way to determine the proper: value of the dummy load R afterthe other parameters are chosen, to view he. q tas wav across h .ssmda y a d a j the resistance of the dummy load-until the areas are equal dthe -C-l e iszem-tf. b a

This method of determining the resistive value of the dummy load R will be especially helpful in maintaining the p p p atio fif 9m. ci uit f ri nitia sign, for it will easily indicate when an imbalance of parameters has arisen by showing other than a zero D.C. level. Such imbalance may be caused by aging or defective portions in the pulse sources, in the transformer itself, or in the secondary circuit. To correct a minor imbalance, the resistance of the dummy load needs to be adjusted only slightly. If, during the operation of the circuit, it is desired to purposely change the recovery time while maintaining the other parameters constant, or to change some of the parameters while maintaining the same recovery time, or a combination of the two, proper parameter balance can be assured by viewing the voltage waveform after the circuit alterations and then adjusting the resistance of the dummy load until the zero D.C. level is again obtained.

Although we have found it convenient to adjust only the dummy load R while holding the other parameters constant, it is appreciated that the other parameters, either alone or in combination with the dummy load, can be adjusted to obtain and maintain. a particularly desired duty factor.

There has thus been ,described'a pulse transformer circuit capable of operating with a very large duty factor which is attained by rapidly coercing the neutralization of the transformer in a'predeterminable time. The recovery time thereby obtained may be substantially shorter than an information pulse to the circuit and is settable by adjusting one component value.

Although we have chosen to call the short duration pulses from the source I neutralization pulses, since at their termination the magnetic field of the transformer is in a neutral condition and the transformer can then properly accept and transmit the next information pulse, it would be equally correct to call them deenergization pulses, since at their termination the level of the energy in the transformer 'is zero. In asimilar vein, since these pulses coerce the rapid .recovery of the transformer, they might be named recovery pulses.

While we have above described the principles of our invention in connection with specific circuitry, it isito be understood that this description is presented as an example only and not as a limitation to our invention, the scope of which is set forth in the accompanying claims.

We claim: I

1. A circuit causing the rapid recovery of a pulse transformer comprising:

a transformerhaving a bisegmented primary coil and a secondarycoil,

a first driving source coupled to one segment of said primary' coil anda second driving source coupled to the'other segment of said primary coil,

said driving sources producing mutually exclusive pulses which appear at the secondary coil with opposite polarities, and cause thereacross tWo distinct voltages with their associated waveforms,

a load resistor in'series with a first diode connected across said secondary coil, 7

said first diode poled for conduction toward said load,

a second resistor connected across the secondary coil,

a series combination of a third resistor and a second diode also connected across said secondary coil,

'said second diode poled for conduction opposite said first diode, and

i said second driving source an said third resistor having selected values whichcause said two voltage waveforms to encompass equal areas.

2. A pulse transformer circuit comprising:

a primary coil and a secondary coil,

a source of mutually exclusive current pulses of opposite phases connected to said primary coil and eliciting magnetizing'currents in said transformer,

any two of said pulses which have opposite phases having different durations, j

a plurality of loads each connected across said secondary coil in parallel to each other,

two of said loads being phase sensitive to said pulses in opposition to each other and also having different impedances,

the greater impedance magnitude of said loads being sensitive to the shorter of said pulses,

such that, at the respective terminations ofsaid pulses,

the magnetizing currents due to said pulses of opposite phase have equal and opposite magnitudes.

3. A circuit enabling the rapid recovery of a pulse transformer comprising:

a primary coil and a secondary coil,

a driving source coupled to said primary coil and operative to supply time exclusive current pulses to opposite ends of said primary coil, and thereby creating magnetic fields in .said transformer,

a first load coupled across said secondary coil,

a second load coupled across said secondary coil and parallel to said first load,

unidirectional current conducting means coupling pulses from said driving source to said loads such that one load is isolated from said pulses when the other load is being driven,

said-magnetic field created by a pulse to said second load being, at the termination of said pulse, equal to the decayed magnitude of the magnetic field resulting from the previously applied pulse to said first load.

. 4. A circuit according to claim 3 wherein said uni-. directional current conducting means comprises a pair of oppositely poled diodes, each connected to one of said loads, and successive of said time exclusive pulses having different amplitudes.

5. In a circuit rapidly neutralizing a pulse transformer:

a polarity alternating current source coupled to the input of said transformer,

a first and a second series combination of a diode and a lumped resistance,

each said combination being coupled across the output of the transformer parallel to the other,

said diodes being poled oppositely and said resistance values having different magnitudes,

whereby after each alternation of current the transformer returns to a neutralized condition.

6. A circuit according toclaim 5 wherein consecutive pulses from said current source are of different duration,

'7. In a circuit for rapidly deenergizing a pulse transformer;

source means coupled to the input of said transformer for producing information pulses and transformer ,deenergizationpulses,

said transformer deenergization pulses being produced in the interval between successive ones of said information pulses and having a duration shorter than said information pulses,

a plurality of loads coupled in parallel across the output of said transformer, V

at least one of said loads exclusively driven by said information pulses and at least another of said loads exclusively driven by said transformer deenergization pulses,

said deenergization pulses appearing across the output of said transformer with a polarity opposite from that of said information pulses,

such that at the termination of any deenergization pulse a substantially zero energy level is attained in the transformer.

8. A circuit for Iapidly deenergizing a pulse transformer comprising: i at least two parallel load resistors of different value connected across the output of said transformer, source means of information pulses coupled'to the smaller valued resistor,

source means of transformer deenergization pulses l coupled to the larger valued resistor,

said source means providing respectively to said loads, during successive time periods, an information pulse and a deenergization pulse each of different duration and polarity to periodically cause, by each of said deenergization pulses, the energy stored in the transformer, as a consequence of the transmission of each of said information pulses, to attain a zero reference level. 9. A circuit for use with a pulse transformer supplying pulses of a given polarity and duration to a load of given impedance comprising: a

a unidirectional current conducting element between said transformer and said load, a source of recovery pulses coupled to the primary of said transformer, said recovery pulses provided alternatively with said supplied pulses and having a different duration and opposite polarity from said supplied pulses, a unidirectional current conducting path for said recovery pulses, said path having a greater impedance than said load, whereby after a supplied pulse and at the termination of a recovery pulse said transformer will be recovered. 10. In a pulse transformer circuit to coerce the rapid recovery of the transformer:

means providing current pulses to the input of said transformer, means coupled to the output of said transformer directing successive of said pulses to alternating paths, each of said paths containing a lumped impedance of a different magnitude, the pulses directed to thelarger of said impedances being shorter than those directed to the other impedance and coercing the recovery of the transformer from a state induced by the pulses directed to the other of said impedances, said coercion being accomplished in a time equal to 10 the duration of a pulse directed to the larger of said impedances. 11. A circuit for rapidly dissipating energy stored in a pulse transformer comprising:

a pulse transformer having a primary winding and a secondary winding, said primary winding being adapted to receive a number of successive information current pulses, source means providing neutralizing current pulses to said primary winding intermediate said information pulses and causing a magnetizing current of a direction opposite to the magnetizing current caused by said information pulses, a first operative load resistor connected in series with a first diode across said secondary winding, a second dummy load resistor connected in series with a second diode across said secondary winding, said second diode being poled oppositely to said first diode, said second dummy load resistor having a value selected to enable the magnetizing current due to said neutralizing current pulses to be, at the end of each of said neutralizing current pulses, substantially equal and opposite to the magnetizing current then exist ing due to said information current pulses, whereby said transformer has its energy rapidly decreased towards zero. 12. A circuit as defined in claim 11 further including a third damping resistor connected across said secondary winding to prevent ringing, said third resistor coacting with said second resistor to form a load for said neutralizing pulses.

No references cited.

MILTON O. HIRSHFIELD, Primary Examiner. 

1. A CIRCUIT CAUSING THE RAPID RECOVERY OF A PULSE TRANSFORMER COMPRISING: A TRANSFORMER HAVING A BISEGMENTED PRIMARY COIL AND A SECONDARY COIL, A FIRST DRIVING SOURCE COUPLED TO ONE SEGMENT OF SAID PRIMARY COIL AND A SECOND DRIVING SOURCE COUPLED TO THE OTHER SEGMENT OF SAID PRIMARY COIL, SAID DRIVING SOURCES PRODUCING MUTUALLY EXCLUSIVE PULSES WHICH APPEAR AT THE SECONDARY COIL WITH OPPOSITE POLARITIES, AND CAUSE THEREACROSS TWO DISTINCT VOLTAGES WITH THEIR ASSOCIATED WAVEFORMS, A LOAD RESISTOR IN SERIES WITH A FIRST DIODE CONNECTED ACROSS SAID SECONDARY COIL, SAID FIRST DIODE POLED FOR CONDUCTION TOWARD SAID LOAD, A SECOND RESISTOR CONNECTED ACROSS THE SECONDARY COIL, A SERIES COMBINATION OF A THIRD RESISTOR AND A SECOND DIODE ALSO CONNECTED ACROSS SAID SECONDARY COIL, SAID SECOND DIODE POLED FOR CONDUCTION OPPOSITE SAID FIRST DIODE, AND SAID SECOND DRIVING SOURCE AN SAID THIRD RESISTOR HAVING SELECTED VALUES WHICH CAUSE SAID TWO VOLTAGE WAVEFORMS TO ENCOMPASS EQUAL AREAS. 